Efficiently matches random graphs with inhomogeneous edge probabilities.
problem Matching latent vertex correspondence between two correlated random graphs with inhomogeneous edge probabilities.
method Inspired by Ding et al. (2021), an efficient matching algorithm is developed with conditions on minimal average degree and minimal correlation.
result An efficient matching algorithm is obtained as long as the minimal average degree is at least Ω(log2n) and the minimal correlation is at least 1−O(log−2n). Polynomial-time algorithm matches correlated random graphs with non-vanishing correlation.
problem Matching correlated random graphs with non-vanishing edge correlation.
method Iterative algorithm for polynomial-time recovery of latent matching.
result Algorithm succeeds in recovering latent matching as long as edge correlation is non-vanishing.
Graph matching in noisy environments with Markovian errors.
problem Graph matching under time-dependent Markovian noise.
method Introduced edgelighter error model and analyzed graph matching thresholds.
result Graph matching thresholds and mixing times are of order Θ(n2logn) for Erdős-Rényi graphs, and O(nαlogn) for Stochastic Block Model graphs. Graph matching with feature vectors is solved using a two-layer graph neural network.
problem Graph matching in the presence of sparse binary features.
method Two-layer graph neural network with graph structure.
result Graph neural network can recover correct mapping with high probability under certain conditions.
We present a parallelized bijective graph matching algorithm that leverages seeds and is designed to match very large graphs. Our algorithm combines spectral graph embedding with existing state-of-the-art seeded graph matching procedures. We justify our approach by proving that modestly correlated, large stochastic blo…
Paper tackles robust graph matching in dense graphs with AMP type algorithm.
problem Matching recovery between correlated Gaussian Wigner matrices with adversarial perturbations.
method Approximate Message Passing (AMP) type iterative algorithm with time-dependent matrix multiplication.
result Algorithm succeeds in polynomial time for non-vanishing correlation and small perturbations.
Study on matching nodes between graphs to preserve edges, focusing on limits and algorithms.
problem Matching nodes between graphs to preserve most edges, especially in random graphs.
method Investigates fundamental limits and designs algorithms to recover alignments in planted graphs.
result High probability guarantees on the success or failure of graph alignment algorithms.
Study sharpens threshold for matching correlated graphs without labels.
problem Matching latent vertex correspondences in correlated random graphs.
method Analyzes information-theoretic limits for correct vertex matching in sub-sampled graphs.
result Establishes a sharp information-theoretic threshold for vertex matching recovery.
OmniMatch algorithm perfectly matches graphs without edge correlation.
problem Graph matching in the absence of edge correlation.
method OmniMatch algorithm for seeded multiple graph matching.
result OmniMatch aligns O(sα) unseeded vertices across multiple networks efficiently and perfectly. In this work we study the degree distribution, the maximum vertex and edge flow in non-uniform random Delaunay triangulations when geodesic routing is used. We also investigate the vertex and edge flow in Erdös-Renyi random graphs, geometric random graphs, expanders and random k-regular graphs. Moreover we show that …
Given a pair of graphs with the same number of vertices, the inexact graph matching problem consists in finding a correspondence between the vertices of these graphs that minimizes the total number of induced edge disagreements. We study this problem from a statistical framework in which one of the graphs is an errorfu…
Adding random features to GNNs improves their performance.
problem Limitations of GNNs in distinguishing graphs and learning efficient algorithms.
method Adding random features to each node in GNNs.
result Random features enable GNNs to learn optimal algorithms for graph problems.
Efficiently matches subgraphs in noisy data without node labels.
problem Subgraph isomorphism in noisy, real-valued graphs.
method Two-step approach: extract topology, then expand matches.
result Realistically sub-linear computational efficiency, robustness to noise.
This paper resolves the all-or-nothing phase transition in graph matching.
problem Recovering vertex correspondence between edge-correlated random graphs.
method Analysis of mutual information, truncated second-moment computation, and maximum likelihood estimator.
result Sharp thresholds for correct matching in both dense and sparse graphs.
This paper tackles matching two complete graphs with correlated edge weights in geometric models.
problem Matching two complete graphs with edge weights correlated through latent geometries.
method Derives an approximate maximum likelihood estimator for recovering hidden vertex correspondence.
result The estimator provably achieves perfect recovery under certain noise conditions.
Improved graph matching algorithm robust to noise.
problem Finding a bijection between vertex sets of two graphs.
method Uses multistage signature vectors to match vertices.
result Recover matching exactly with high probability for α≤1/(loglogn)C. GraphMoE generates random graphs using neural networks and graphlets.
problem Learning generative models for random graphs.
method GraphMoE uses a neural network trained with graphlets and subgraph counts to match the distribution of random graphs.
result GraphMoE can generate graphs that mimic various real-world datasets and fool graph classifiers.
Algorithm matches vertices of correlated Erdős-Rényi graphs efficiently.
problem Graph matching in correlated Erdős-Rényi graphs.
method Counting chandeliers to extract graph correlation.
result Correctly matches all but a vanishing fraction of vertices with high probability.
The paper introduces heterogeneous manifolds for better graph embeddings.
problem Graph embeddings in Euclidean spaces often fail to capture the curvature of real-world graphs.
method The authors propose heterogeneous rotationally-symmetric manifolds with a radial dimension to account for varying curvature.
result The method improves graph embeddings by better preserving high-order structures and heterogeneous random graphs.
Paper solves graph matching for correlated Erdős--Rényi graphs.
problem Matching vertices of correlated Erdős--Rényi graphs.
method Polynomial-time algorithm based on comparison of partition trees.
result Exact matching achieved with high probability.
Random graph matching refers to recovering the underlying vertex correspondence between two random graphs with correlated edges; a prominent example is when the two random graphs are given by Erdős-Rényi graphs G(n,nd). This can be viewed as an average-case and noisy version of the graph isomorphism problem.…
We present an alternate formulation of the partial assignment problem as matching random clique complexes, that are higher-order analogues of random graphs, designed to provide a set of invariants that better detect higher-order structure. The proposed method creates random clique adjacency matrices for each k-skeleton…
Improved graph generation model for small organic molecules.
problem Graph generation models struggle with matching training distributions and require expensive graph matching.
method Introduced a message passing neural network into the GVAE's encoder and decoder.
result Demonstrated improved graph generation for small organic molecules.
Random weights in GNNs match learned weights in performance.
problem Feature rank collapse in GNNs.
method Replacing learned weights with random weights.
result Random weights achieve comparable performance to learned weights, reducing training time and memory usage.
New spectral algorithm estimates random graph parameters robustly against corrupted nodes.
problem Estimating the parameter of an Erdős-Rényi random graph with adversarial corruption.
method Spectral algorithm designed for computational efficiency, with an inefficient but information-theoretic alternative.
result Achieves optimal error rate up to logarithmic factors, matching statistical lower bounds.
Graph kernels are widely used for measuring the similarity between graphs. Many existing graph kernels, which focus on local patterns within graphs rather than their global properties, suffer from significant structure information loss when representing graphs. Some recent global graph kernels, which utilizes the align…
While a wide range of interpretable generative procedures for graphs exist, matching observed graph topologies with such procedures and choices for its parameters remains an open problem. Devising generative models that closely reproduce real-world graphs requires domain knowledge and time-consuming simulation. While e…
Graph spectra have been successfully used to classify network types, compute the similarity between graphs, and determine the number of communities in a network. For large graphs, where an eigen-decomposition is infeasible, iterative moment matched approximations to the spectra and kernel smoothing are typically used. …
Graph alignment in two correlated random graphs refers to the task of identifying the correspondence between vertex sets of the graphs. Recent results have characterized the exact information-theoretic threshold for graph alignment in correlated Erdős-Rényi graphs. However, very little is known about the existence of e…
GCNs distinguish graph models based on embeddings, but depth matters.
problem GCNs distinguish between different random graph models.
method Investigated the power of GCNs of varying depths to distinguish between graph models.
result GCNs with logarithmic depth can distinguish certain graphons, but simpler architectures suffice for others.
BWFlow improves graph generation by smoothly interpolating graph components.
problem Disjoint modeling of graph nodes and edges leads to irregular and non-smooth probability paths.
method Modeling graphs as MRFs and using optimal transport displacement for a smooth probability path.
result BWFlow achieves better training convergence and efficient sampling in graph generation.
Network complexity has been studied for over half a century and has found a wide range of applications. Many methods have been developed to characterize and estimate the complexity of networks. However, there has been little research with statistical guarantees. In this paper, we develop a statistical theory of graph c…
Study reconstructs hidden perfect matchings in random graphs with specific edge weights.
problem Reconstructing hidden perfect matchings in random weighted bipartite graphs.
method Analyzes the maximum likelihood estimator for matching reconstruction under different probability distributions of edge weights.
result Sharp threshold and infinite-order phase transition in reconstruction error for different probability distributions.
Ricci curvature was proposed by Ollivier in a general framework of metric measure spaces, and it has been studied extensively in the context of graphs in recent years. In this paper we prove upper bounds for Ollivier's Ricci curvature for bipartite graphs and for the graphs with girth at least 5. We also prove a genera…
Paper extends tail bounds to high-dimensional random objects on Riemannian manifolds.
problem Need for tail bounds in high-dimensional data.
method Random walks on graph approximating the manifold, ensuring spectral similarity.
result Derived tensor Chernoff bound for Riemannian manifolds.
SIGMA model improves graph matching across various applications.
problem Graph matching problem in different domains.
method Stochastic Iterative Graph Matching (SIGMA) model with multi-step refinement and dummy nodes.
result SIGMA produces significantly improved graph matching results compared to state-of-the-art models.
Method finds multiple noisy graph templates in large graphs.
problem Finding multiple graph templates in noisy large graphs.
method Iteratively penalizes node-pair similarity matrix in matched filter algorithm.
result Method can sequentially discover multiple templates under mild model conditions.
Paper proposes a new method for population-wise matching of sulcal graphs.
problem Challenges in matching cortical fold variations across individuals.
method Population-wise multi-graph matching of sulcal graphs.
result Effectiveness of multi-graph matching in obtaining consistent labeling of sulcal basins.
Large unweighted directed graphs are commonly used to capture relations between entities. A fundamental problem in the analysis of such networks is to properly define the similarity or dissimilarity between any two vertices. Despite the significance of this problem, statistical characterization of the proposed metrics …
We study a well known noisy model of the graph isomorphism problem. In this model, the goal is to perfectly recover the vertex correspondence between two edge-correlated Erdős-Rényi random graphs, with an initial seed set of correctly matched vertex pairs revealed as side information. For seeded problems, our result pr…
Riemannian metric matching learns the geometry of high-dimensional datasets using neural networks.
problem Estimating the geometry of high-dimensional datasets from samples
method Riemannian metric matching using neural networks
result Riemannian metric matching rivals or improves k-NN-based diffusion geometry estimators Given two graphs, the graph matching problem is to align the two vertex sets so as to minimize the number of adjacency disagreements between the two graphs. The seeded graph matching problem is the graph matching problem when we are first given a partial alignment that we are tasked with completing. In this paper, we m…
This paper sets thresholds for recovering vertex correspondences in partially correlated graphs.
problem Recovering hidden vertex correspondences in partially correlated graphs.
method Proposed partially correlated Erdős-Rényi graphs model; information-theoretic thresholds; correlated functional digraphs.
result Optimal rates for partial and exact recovery of vertex correspondences.
NeuroMatch efficiently matches subgraphs in large graphs using neural networks.
problem Determining the presence and location of a query graph in a large target graph.
method NeuroMatch decomposes graphs into subgraphs, embeds them using graph neural networks, and matches them directly in the embedding space.
result NeuroMatch is 100x faster and 18% more accurate than existing methods.
Proposes methods to recover labels from shuffled networks using graph averages.
problem Recovering labels from a shuffled network using graph averages.
method Cluster networks into classes, then match the new graph to cluster-averages, minimizing the graph matching objective function.
result Higher fidelity matching performance when clustering networks into different classes.
Optimizes experiment design for causal structure learning in linear models with cycles.
problem Causal structure learning from combined observational and interventional data in linear non-Gaussian cyclic models.
method Combinatorial characterization of equivalence classes, adaptive stochastic optimization, greedy policy with near-optimal performance guarantee, sampling-based estimator for reward function.
result Optimal experiment design reduces the equivalence class of causal graphs to a single true graph with a small number of interventions.
We present a novel approximate graph matching algorithm that incorporates seeded data into the graph matching paradigm. Our Joint Optimization of Fidelity and Commensurability (JOFC) algorithm embeds two graphs into a common Euclidean space where the matching inference task can be performed. Through real and simulated …
The paper bounds crossing numbers of dense graphs on surfaces.
problem Estimating the minimum number of edge crossings for dense graphs on surfaces.
method Proved lower and upper bounds on crossing numbers, providing explicit families of surfaces.
result Upper and lower bounds on crossing numbers match up to constant factors.